CN110649624A - Power flow parallel computing method for electric power system - Google Patents

Power flow parallel computing method for electric power system Download PDF

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CN110649624A
CN110649624A CN201911091208.8A CN201911091208A CN110649624A CN 110649624 A CN110649624 A CN 110649624A CN 201911091208 A CN201911091208 A CN 201911091208A CN 110649624 A CN110649624 A CN 110649624A
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宋晓喆
孙福寿
李振元
李雪
魏国
姜涛
陈厚合
李国庆
张儒峰
李筱婧
于洋
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State Grid Jilin Electric Power Corp
Northeast Electric Power University
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State Grid Jilin Electric Power Corp
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The invention discloses a power flow parallel computing method of a power system, which comprises the following steps: 1) performing power flow calculation on the power system based on a cow-pulling method to obtain a nonlinear power flow equation, and obtaining a power flow correction equation set according to a successive linear principle; 2) solving a power flow correction equation set based on a BICGSAB method, obtaining a two-stage preprocessing algorithm consisting of improved PPAT preprocessing and improved Jacobi preprocessing, and preprocessing a coefficient matrix, namely a Jacobi matrix, of the power flow correction equation set so as to improve the convergence of the BICGSAB method; 3) and running the parallel computing process in the step 2) based on the CPU-GPU heterogeneous platform. The method has the advantages of high calculation speed and high robustness, and is suitable for systems which cannot be converged by the traditional method; the method can realize the rapid solution of the power flow of the power system.

Description

Power flow parallel computing method for electric power system
Technical Field
The invention relates to the field of power systems, in particular to a power flow parallel computing method of a power system.
Background
The load flow calculation is the basis of the problems of safety and stability analysis, fault calculation, economic dispatching and the like of the power system. Accurate and quick load flow calculation results are important guarantees for safe and reliable operation of the power grid. With continuous expansion of interconnection scale of regional power grids, large-scale grid connection of renewable energy sources and large-scale application of power electronic equipment, the scale and complexity of load flow calculation of a power system are increased sharply. Meanwhile, the intelligent process of the power grid is continuously deepened, the fine operation requirement of the power grid is continuously improved, and operators have higher requirements on the tidal current calculation precision and efficiency of the power system.
The Newton method is the most widely adopted method for the load flow calculation of the current power system, and the method converts the solution of a nonlinear load flow equation into the solution of a linear correction equation set based on the successive linear approximation principle[1]. The solution of the correction equation set is the most time-consuming part in the cow-drawn method, and accounts for about 80 percent of the time-consuming part of the whole trend calculation[2]. Therefore, reducing the partial solution time is an improvementThe key of the calculation efficiency of the power flow of the power-rise system is.
Currently, the correction equation set is solved mainly by a direct method and an iterative method. Direct process[3]Based on sparse matrix decomposition technology, the solution of each correction is solved one by one, and in the process, each correction has strong correlation, so that parallelization of correction equation set solution is not easy to realize[4]. Meanwhile, when the jacobian matrix is decomposed by the direct method, the filling problem of non-zero elements exists, and when the system scale is increased, the data storage capacity is greatly increased, so that the rapid solution of the large-scale interconnected power system tide is not facilitated. Compared with a direct method and an iterative method, when the correction equation set is solved, the solution vector of the correction quantity is continuously corrected, so that the solution vector of the correction quantity gradually approaches to the actual solution vector of the tidal current equation. The process mainly relates to sparse matrix and inter-vector operation, has weak data correlation and good parallel characteristic, and is suitable for processing high-dimensional correction equation sets.
The iteration method mainly comprises a classical iteration method and a Krylov subspace iteration method. The classical iteration method has poor convergence and is less applied at present; the Krylov subspace iteration method has been applied to the fields of load flow calculation, small interference analysis, transient stability analysis and the like due to excellent convergence and numerical stability[5]-[8]. However, each Krylov subspace method has a certain application range, and when the Krylov subspace method is adopted to solve the power flow correction equation set, the commonly used Krylov subspace method is a Generalized Minimum Residual Error (GMRES) method and a bicgsab method for the asymmetric feature of the jacobian matrix. The GMRES method can accurately realize the solution of the correction equation set, has good convergence, but needs long recursion when constructing the Krylov subspace substrate, and leads to the rapid increase of iteration times, data storage capacity and calculation amount when the system scale is increased, thereby being not beneficial to the rapid solution of the high-dimensional correction equation set. Compared with the GMRSE method, the BICGSAB method is applied to the solution of a high-dimensional correction equation set by the advantages of storage space stability, short recurrence and the like. However, when the BICGSAB method is adopted to solve the correction equation set, the power flow Jacobian matrix needs to be preprocessed[9]Compressing the distribution interval of its characteristic values, fromThereby improving the astringency of the BICGSAB method. The design of the preprocessor still restricts the application of the BICGSAB method to the power system power flow parallel computation at present.
How to quickly and accurately realize the load flow calculation of the power system is the key point of current research.
Disclosure of Invention
The invention provides a power system load flow parallel computing method, which ensures the correctness of load flow computing results, has higher computing speed and stronger robustness for large-scale systems, and can be suitable for systems which cannot be converged by some traditional methods; compared with the power flow algorithm which is based on the CPU-GPU heterogeneous platform and adopts the classic ILU (0) preprocessor or the single preprocessor, the method also has obvious advantages, can realize the rapid solution of the power flow of the power system, and is described in detail in the following:
a power system power flow parallel computing method, the method comprising the steps of:
1) performing power flow calculation on the power system based on a cow-pulling method to obtain a nonlinear power flow equation, and obtaining a power flow correction equation set according to a successive linear principle;
2) solving a power flow correction equation set based on a BICGSAB method, obtaining a two-stage preprocessing algorithm consisting of improved PPAT preprocessing and improved Jacobi preprocessing, and preprocessing a coefficient matrix, namely a Jacobi matrix, of the power flow correction equation set so as to improve the convergence of the BICGSAB method;
3) and running the parallel computing process in the step 2) based on the CPU-GPU heterogeneous platform.
Wherein the improved PPAT pretreatment specifically comprises the following steps:
by taking the characteristics that a block diagonal matrix B consisting of active and reactive Jacobian matrixes B 'and B' in the rapid decoupling load flow algorithm can be used as a preprocessor of a Jacobian matrix A as reference:
Figure BDA0002266913570000021
wherein B is an approximate Schur complement of A; let M0Is formed by ATSub-square matrix H ofT、LTThe block diagonal matrix is composed of:
Figure BDA0002266913570000022
in the formula, M0An approximate Schur complement of A; with M0As MPInitial sparse mode of (1), finish MPThe structure of (1), namely, the improved PPAT preprocessor; mPThe diagonal-like dominance characteristic of A is kept, but the quantity of non-zero elements is half of that of A;
wherein, the first stage of the two-stage pretreatment specifically comprises the following steps:
improved PPAT preprocessor MPExpressed as:
Figure BDA0002266913570000031
the modified PPAT pre-processing equation is:
MPAΔx＝MPb
the coefficient matrix a of the correction amount deltaxPComprises the following steps:
Figure BDA0002266913570000032
wherein M isP1、MP4For improving PPAT preprocessor MPA is a Jacobian matrix, b is active and reactive variable quantity, AP1、AP2、AP3、AP4Four block matrices of the newly formed coefficient matrix after preprocessing.
Wherein the improved Jacobi pretreatment specifically comprises the following steps:
coefficient matrix APComposed of four block matrices, sub-matrix AP2、AP3Not square but full rank sub-square AP2 *、AP3 *And A isP2 *、AP3 *Has similar diagonal dominance; a is to beP1、AP4、AP2 *、AP3 *Is taken out and is according to it at APOf (1), reconstituting the sparse matrix AJ，AJCan be described as a four-block matrix, shaped as:
in the formula, S, T*、U*W is a diagonal matrix, and diagonal elements of each matrix meet the following conditions:
Figure BDA0002266913570000034
in the formula, AJThe matrix is a highly sparse matrix, sub-matrices S and W are diagonal matrices, and non-zero elements of rows and columns in the sub-matrices T and U are not more than 1 at most; to AJInversion to obtain an improved Jacobi preprocessor MJ；
Wherein, the second stage of the two-stage pretreatment specifically comprises the following steps:
the modified equation set is further modified by a Jacobi preprocessor as follows:
APMJy＝MPb
coefficient matrix A of the quantity y to be solvedPJComprises the following steps:
APJ＝APMJ
Δx＝MJy
wherein M isJTo improve Jacobi pre-treatment.
The technical scheme provided by the invention has the beneficial effects that:
1. the method can realize accurate solution of the power system power flow, and compared with the traditional Newton method power flow calculation result, the relative error between the two is extremely small;
2. the invention provides an improved PPAT pretreatment and an improved Jacobi pretreatment, and provides a two-stage pretreatment method combining the PPAT pretreatment and the Jacobi pretreatment, the pretreatment method is used for pretreating a Jacobi matrix, the characteristic value distribution of the Jacobi matrix can be effectively improved, the convergence and the robustness of a BICGSAB method are improved, the solving efficiency of a correction equation set is greatly improved, and the load flow calculation efficiency is further effectively improved;
3. compared with the classic ILU (0) preprocessing power flow algorithm, the ILU (0) preprocessing power flow algorithm has the advantages that the calculation speed is higher, the calculation efficiency is higher, the robustness is stronger, the data correlation of the ILU (0) preprocessing method is strong, parallel calculation is not facilitated, and the two-stage preprocessing method has good parallel characteristics and is suitable for acceleration by means of a CPU-GPU heterogeneous platform;
4. compared with other commonly preprocessed power flow algorithms, the two-stage preprocessed power flow algorithm provided by the invention has the advantages of fewer iteration times in a system with a larger scale, less calculation time consumption and better adaptability, and provides a feasible idea for quickly solving the power flow of a large-scale interconnected power system.
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Fig. 1 is a flow chart of a power system power flow parallel computation method;
FIG. 2 is a diagram of the algorithm framework of the present invention;
FIG. 3 is a bar graph of the voltage amplitude of the PQ node at maximum error;
FIG. 4 is a comparison histogram of calculation time.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
Example 1
In order to realize the fast and accurate solution of the power flow of the power system, the embodiment of the invention provides a power flow parallel computing method of the power system, which comprises the following steps:
101: performing power flow calculation of the power system based on a cow pulling method to obtain a nonlinear power flow equation, and obtaining a power flow correction equation set according to a successive linear principle;
102: solving a power flow correction equation set based on a BICGSAB method, obtaining a two-stage preprocessing algorithm consisting of improved PPAT preprocessing and improved Jacobi preprocessing, and preprocessing a coefficient matrix, namely a Jacobi matrix, of the power flow correction equation set so as to improve the convergence of the BICGSAB method;
103: and the parallelization of the two-stage preprocessing BICGSAB method for solving the correction equation set is realized on the basis of the CPU-GPU heterogeneous platform, and the rapid solution of the power system load flow is realized.
In summary, in the embodiment of the present invention, through the steps 101 to 103, based on the CPU-GPU heterogeneous platform, the correction equation set is solved in parallel by combining the two-stage preprocessing and the bicgsab method, so that the power flow calculation efficiency of the power system is improved.
Example 2
The general framework of the embodiment of the invention is as shown in fig. 2, and can be divided into a CPU part and a GPU part, and the parallel acceleration is completed by the GPU part.
Wherein, the GPU part mainly comprises:
the method adopts a BICGSAB method to solve the process of the correction equation set after two-stage preprocessing, and the process is called inner layer iteration in the embodiment of the invention;
wherein, the CPU part mainly includes:
the flow control of the cow pulling method comprises the processes of forming a correction equation set, forming a preprocessor, correcting an iteration variable, judging convergence and the like. The embodiment of the invention refers to the process as outer layer iteration, which is essentially Newton method flow calculation iteration process.
The scheme in embodiment 1 is further described below with reference to specific calculation formulas and drawings, and is described in detail below:
the following embodiments of the present invention all use linear correction equation set (1) as an example to describe how to construct a preprocessor to preprocess a jacobian matrix.
AΔx＝b (1)
In the formula, A is a Jacobian matrix, Δ x is a correction amount, and b is a column vector consisting of a voltage amplitude and a phase angle.
The improved PPAT preprocessor is improved based on the PPAT preprocessor.
Transpose A of Jacobian matrix ATComprises the following steps:
Figure BDA0002266913570000051
PPAT preprocessor is directed to construction with ATHave an approximate inverse of the same sparse pattern. Details of the construction of PPAT preconditioners are described in the literature [10]. The number of non-zero elements in some rows of the jacobian matrix a is larger, which results in a larger required memory space. In order to reduce data storage capacity, the invention simplifies the sparse mode of the PPAT preprocessor properly, and provides an improved PPAT preprocessor which is marked as MPThe concrete improvement is as follows:
by taking the characteristics that a block diagonal matrix B consisting of active and reactive Jacobian matrixes B 'and B' in the rapid decoupling load flow algorithm can be used as a good preprocessor of a Jacobian matrix A as follows:
Figure BDA0002266913570000052
wherein B is an approximate Schur complement of A. Let M0Is formed by ATSub-square matrix H ofT、LTThe block diagonal matrix is composed of:
in the formula, M0Also an approximate Schur complement of a. With M0As MPInitial sparse mode of (1), finish MPI.e., an improved PPAT preconditioner. MPThe diagonal-like dominance characteristic of A is maintained, but the number of the non-zero elements is about half of that of A, and the storage amount and the calculation amount of data are reduced.
Improved PPAT preprocessor MPCan be expressed as:
Figure BDA0002266913570000062
the modified PPAT pre-processing equation is:
MPAΔx＝MPb (6)
the coefficient matrix A of the correction amount Deltax in equation (6)PComprises the following steps:
Figure BDA0002266913570000063
after the formula (1) is subjected to the PPAT pretreatment, the solution of the correction equation set is converted into the solution of the linear equation set shown in the formula (6) and having the same solution as the formula (1).
The invention according to APAnd the similar diagonal dominance of the sub-matrix, properly expands the sparse mode of the Jacobi preprocessor, and provides an improved Jacobi preprocessor which is marked as MJThe concrete improvement is as follows:
from equation (7), the coefficient matrix APComposed of four block matrices, although its sub-matrix AP2、AP3Not a square matrix, but AP2、AP3There is a full rank sub-matrix AP2 *、AP3 *And A isP2 *、AP3 *Has similar diagonal dominance. Thus, AP1、AP4、AP2 *、AP3 *Is taken out and is according to it at APOf (1), reconstituting the sparse matrix AJ。AJCan be described as a four-block matrix, like:
Figure BDA0002266913570000064
in the formula, S, T*、U*And W are diagonal matrixes. Each matrix diagonal element satisfies:
Figure BDA0002266913570000065
in the formula, AJThe matrix is a highly sparse matrix, the sub-matrices S and W are diagonal matrices, and the number of non-zero elements of each row and column in the sub-matrices T and U is not more than 1 at most. To AJInversion is carried out, and the improved Jacobi preprocessor M is obtainedJ. The operation does not introduce any new non-zero elements and therefore does not cause a change in the amount of data storage. In addition, the method can be used for producing a composite material，MJThe construction process of (2) mainly relates to the operation of a highly sparse matrix, and compared with a Jacobi preprocessor, the improved method has the advantage of little increased calculation amount.
Formula (6) after modified Jacobi pretreatment is:
APMJy＝MPb (10)
the coefficient matrix A of the quantity y to be solved in (10)PJComprises the following steps:
APJ＝APMJ (11)
at this time, the column vector y obtained by solving equation (11) is not the solution Δ x of the correction equation system shown in equation (1), but both satisfy:
Δx＝MJy (12)
for simplicity, the above-mentioned process of processing the Jacobi matrix by using the modified PPAT pre-processor and then using the modified Jacobi pre-processor is referred to as two-stage pre-processing, and the following description is generally made by using the two-stage pre-processing.
The method comprises the following specific steps:
201: reading original node data of the power system, constructing a node admittance matrix, and obtaining G in the formula (1)ij、BijSetting initial values of a node voltage amplitude V and a phase angle delta;
202: setting the iteration number m to be 0 and calculating the precision epsilon1Maximum number of iterations N1；
203: bringing V and delta into formula (1), and determining | | f (x) | non-woven cells<ε1Whether the current is true or not is judged, if yes, the flow calculation of the cow-drawn method is quitted, and the algorithm is converged; otherwise, continuing the following steps;
204: judging whether m reaches a set value N1If yes, quitting the flow calculation of the cow pulling method, and the algorithm is not converged; if not, making m equal to m + 1;
205: obtaining a correction equation set in the form of formula (1);
wherein, step 205 mainly comprises:
1) the power equation of the node of the power system under the polar coordinate is as follows:
Figure BDA0002266913570000071
in the formula, Vi、VjIs the voltage amplitude, delta, of nodes i and jijIs the voltage angle difference of nodes i and j, PiAnd QiThe active and reactive injection quantities of the node i are respectively.
2) Equation (13) may be described in the form of f (x) 0, where x is a column vector of state variables V and δ. Expanding the formula (13) according to Taylor series, and discarding the terms of second order and above to obtain:
Figure BDA0002266913570000072
in the formula (I), the compound is shown in the specification,
Figure BDA0002266913570000073
3) formula (14) can be further described as the form shown in formula (1).
206: solving a correction equation set based on a GPU by adopting a two-stage preprocessing BICGSAB method;
wherein the step 206 comprises:
1) if M is 1, structure MPAnd MJContinuing with step 2); otherwise, skipping the step and directly executing the step 2);
2) using MPAnd MJB, preprocessing A in two stages, and transmitting all parts of the obtained new program group into a GPU;
3) setting an initial value y of y(0)Allowable error e2Solving for the initial residual r0＝MPb-APJy(0)；
4) Selecting
Figure BDA0002266913570000081
So that
Figure BDA0002266913570000082
Generally get
Figure BDA0002266913570000083
And let p1＝r0，k＝1；
5) Computing
Figure BDA0002266913570000084
qk＝rk-1-αkAPJpk，ωk＝(qk,APJqk)/(APJqk,APJqk)；
6) Calculating y(k)＝y(k-1)+αkpk+ωkqk，rk＝qk-ωkAPJqk；
7) If rk||2≤ε2Iteratively converging, and going to step 9); otherwise, continuing to step 8);
8) computing
Figure BDA0002266913570000085
pk+1＝rk+βk(pk-ωkAPJpk) Making k equal to k +1, and going to step 5);
9) solving to obtain delta x(m)。
207: calculating the GPU to obtain delta x(m)Returning to the CPU, the iteration quantities V and δ are corrected, and the process goes to step 203.
In summary, the embodiments of the present invention provide a power system power flow parallel computing method based on the taura method through the above steps 201 to 207 to improve the power flow computing rate.
Example 3
The feasibility verification of the schemes in examples 1 and 2 is performed below with reference to specific fig. 3, fig. 4, and tables 1 and 2, as described in detail below:
the present example was verified and analyzed with different test systems. Except for special description, the calculation precision of the bovine-derived method in the following calculation examples is 0.001, and the calculation precision of the BICGSAB method for solving the correction equation set is 0.001.
In order to test the accuracy of the load flow calculation, the traditional cow pulling method and the load flow calculation results of different test systems of the invention are compared respectively. Fig. 3 shows the magnitude of the PQ node voltage when the error between the PQ node voltage and the node voltage is the maximum, and table 1 details the values and relative errors of the PV node reactive power and the node voltage phase angle obtained by the two algorithms when the error is the maximum. Obviously, as can be seen from fig. 3: for test systems of different scales, the PQ node voltage amplitude calculated by the method is basically consistent with that of the traditional cow-drawn method, and only a tiny error exists between the PQ node voltage amplitude and the traditional cow-drawn method. Further, as can be seen from table 1: for test systems of different scales, the PV node reactive power and the node voltage amplitude obtained by the method are approximately equal to those of the traditional Czochralski method, and the maximum relative error of the PV node reactive power and the node voltage amplitude is less than 0.15%. The method provided by the invention is verified to have higher calculation accuracy in load flow calculation.
TABLE 1 reactive power and Voltage phase Angle at maximum error
Figure BDA0002266913570000086
Figure BDA0002266913570000091
To verify the effectiveness of the method, the method is compared with a trend algorithm based on ILU (0) preprocessing without non-zero element filling, and the results are shown in table 2. The results in table 2 are the average number of iterations with different preprocessing methods when solving the correction equation set.
TABLE 2 number of iterations of the tidal flow Algorithm when different preprocessors are used
Figure BDA0002266913570000092
Note: before and after "/" are the average iteration times of the inner layer pretreatment BICGSAB method for solving the correction equation set and the outer layer bovine pulling method iteration times
The results of comparing the number of iterations of the venlafaxine method in table 2 show that: under the influence of the solving precision of the internal correction equation set, the iteration times of the same system may slightly fluctuate, but can be converged only by iterating 3-6 times normally. The average iteration times of the pretreatment BICGSAB method are compared to obtain the following result: in a system with a smaller scale, the iteration times of the ILU (0) preprocessing BICGSAB method are the least; when the calculation scale is increased to a certain degree (such as 9241 nodes), the iteration number required by the BICGSAB method adopting ILU (0) pretreatment is obviously increased, the iteration number of the BICGSAB method can be better reduced by improving the PPAT pretreatment and the two-stage pretreatment, and the effect of reducing the iteration number by the two-stage pretreatment is most obvious.
It is worth noting that: for large-scale test systems such as case _ ACTIVSG70k where the BICGSAB method fails to converge when ILU (0) pre-processing, modified PPAT pre-processing or modified Jacobi pre-processing is used alone, the two-stage pre-processing is still converged. It can be seen from this that: the method has the advantages of less iteration times and strong robustness, and provides a feasible scheme for quickly solving the power flow of the large-scale interconnected power system.
In order to evaluate the calculation efficiency of the method, fig. 4 compares the load flow algorithm of ILU (0) preprocessing with the calculation time of the method based on the CPU platform and the CPU-GPU heterogeneous platform, respectively. Comparing the calculation time of the power flow algorithm in fig. 4, which respectively adopts ILU (0) preprocessing and two-stage preprocessing on the same platform, it can be known that: in a system with a small scale, the calculation time of an ILU (0) preprocessing power flow algorithm is shortest; with the increase of the system scale, the calculation time consumption of the ILU (0) preprocessing power flow algorithm is increased sharply, the advantages of the two-stage preprocessing power flow algorithm are gradually shown, and the advantages are more obvious when the system scale is larger. The calculation time consumption of the same preprocessed power flow algorithm on the CPU platform and the CPU-GPU heterogeneous platform respectively is compared to know that: for a system with a small scale, the parallel computing time based on the CPU-GPU heterogeneous platform is longer than the serial computing time based on the CPU platform, and the main reason is that the GPU parallel acceleration time is difficult to make up the data interaction time between the CPU and the GPU; when the node scale is increased to about 3000, the advantages of parallel computing based on the CPU-GPU platform are gradually shown, and the larger the system scale is, the more obvious the advantages are. The time-consuming curve calculated by the CPU-GPU heterogeneous platform-based two-stage preprocessing load flow algorithm in fig. 4 can be known as follows: the load flow calculation time of the method approximately presents a linear relation with the system scale, and the change is smooth, which shows that the method has good convergence and scalability.
In order to analyze the acceleration conditions of different preprocessing power flow algorithms, the calculation time consumption of the ILU (0) preprocessing power flow algorithm on the CPU platform is taken as a reference value, the ratio (recorded as an acceleration ratio) of the reference value to the calculation time consumption of other power flow algorithms is counted, the acceleration conditions of the different power flow algorithms relative to the ILU (0) preprocessing power flow algorithm are analyzed, and the results are shown in Table 3. In table 3, if the ILU (0) preprocessed power flow algorithm on the CPU platform does not converge, that is, the acceleration ratio of the power flow calculation has no reference value, only the convergence information of the algorithm is recorded.
TABLE 3 acceleration ratio for different power flow algorithms
Figure BDA0002266913570000101
Figure BDA0002266913570000111
As can be seen from Table 3: for a system with a small scale, the ILU (0) has the least time consumption for preprocessing a power flow algorithm; with the enlargement of the system scale, the advantages of the two-stage preprocessing trend algorithm are gradually shown. In addition, in a large-scale system, although the ILU (0) preprocessing power flow algorithm based on the CPU-GPU heterogeneous platform can improve the power flow calculation efficiency to a certain extent, the acceleration effect is poor, and even compared with a two-stage preprocessing power flow algorithm based on the CPU platform, a large gap still exists.
The two-stage preprocessing load flow algorithm based on the CPU-GPU heterogeneous platform has the highest calculation efficiency, and compared with the ILU (0) preprocessing load flow algorithm based on the CPU platform, the maximum acceleration ratio can reach 40.70 times. For a large-scale test system with the ILU (0) preprocessing power flow algorithm not converged, the method still converges. It can be seen from this that: the method has higher efficiency and stronger robustness when solving the power flow of the large-scale interconnected power system, and can well realize the rapid power flow calculation of the large-scale interconnected power system.
The above analysis shows that: the method is based on a CPU-GPU heterogeneous platform, the parallel solving method combining two-stage preprocessing and the BICGSAB method is adopted in load flow calculation of a large-scale test system, load flow calculation efficiency can be effectively improved, algorithm stability is good, and the advantages of the method are more obvious than those of a traditional load flow calculation method.
Reference to the literature
[1] Tangkunje, dongfushen, songyanghua power system trend algorithm [ J ] based on incomplete LU decomposition preprocessing iteration method, proceedings of china motor engineering, 2017, 37 (S1): 55-62.
[2] Cai for large, chenyurong.imprecise power flow calculation with incomplete LU decomposition preprocessing [ J ] power system automation, 2002, 26 (8): 11-14.
[3] Zhangongjie, sunqin. large sparse linear equation set notation LU decomposition method [ J ] computer engineering and applications, 2007, 43 (28): 29-30.
[4] Liuyang, Zhou Jia Qi, Xie Gui, etc. A large-scale power system equation parallel PCG based on Beowulf cluster solves [ J ]. report on electrotechnics, 2006, 21 (3): 105-111.
[5]Li X，Li F.GPU-based two-step preconditioning for conjugate gradient method in power flow[C].IEEE Power&Energy Society General Meeting，Denver，CO，USA 2015.
[6]Li X，Li F，Clark J M.Exploration of multifrontal method with GPU in power flow computation[C].IEEE Power&Energy Society General Meeting.2013：1-5.
[7]Zhou G，Bo R，Chien L，et al.GPU-accelerated algorithm for on-line probabilistic power flow[J].IEEE Transactions on Power Systems，2017，PP(99)：1-1.
[8]Benzi M.Preconditioning techniques for large linear systems：a survey[J].Journal of Computational Physics，2002，182(2)：418-477.
[9]Yu Z，Huang S，Shi L，et al.GPU-based JFNG method for power system transient dynamic simulation[C].International Conference on Power System Technology.IEEE，2014.
[10] Late lihua, liujie, li dao mei sparse approximate inverse preconditioner and its parallel computation [ J ] computer science, 2000, 23 (3): 255-260.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (3)

1. A power system power flow parallel computing method is characterized by comprising the following steps:
1) performing power flow calculation on the power system based on a cow-pulling method to obtain a nonlinear power flow equation, and obtaining a power flow correction equation set according to a successive linear principle;
2) solving a power flow correction equation set based on a BICGSAB method, obtaining a two-stage preprocessing algorithm consisting of improved PPAT preprocessing and improved Jacobi preprocessing, and preprocessing a coefficient matrix, namely a Jacobi matrix, of the power flow correction equation set so as to improve the convergence of the BICGSAB method;
3) and running the parallel computing process in the step 2) based on the CPU-GPU heterogeneous platform.
2. The power flow parallel computing method of the power system as claimed in claim 1, wherein the improved PPAT preprocessing is specifically:
by taking the characteristics that a block diagonal matrix B consisting of active and reactive Jacobian matrixes B 'and B' in the rapid decoupling load flow algorithm can be used as a preprocessor of a Jacobian matrix A as reference:
Figure FDA0002266913560000011
wherein B is an approximate Schur complement of A; let M0Is formed by ATSub-square matrix H ofT、LTThe block diagonal matrix is composed of:
Figure FDA0002266913560000012
in the formula, M0An approximate Schur complement of A; with M0As MPInitial sparse mode of (1), finish MPThe structure of (1), namely, the improved PPAT preprocessor; mPThe diagonal-like dominance characteristic of A is kept, but the quantity of non-zero elements is half of that of A;
the first stage of the two-stage pretreatment is specifically:
improved PPAT preprocessor MPExpressed as:
Figure FDA0002266913560000013
the modified PPAT pre-processing equation is:
MPAΔx＝MPb
the coefficient matrix a of the correction amount deltaxPComprises the following steps:
Figure FDA0002266913560000014
wherein M isP1、MP4For improving PPAT preprocessor MPA is a Jacobian matrix, b is active and reactive variable quantity, AP1、AP2、AP3、AP4Four block matrices of the newly formed coefficient matrix after preprocessing.
3. The power system load flow parallel computing method according to claim 2, wherein the improved Jacobi preprocessing specifically comprises:
coefficient matrix APComposed of four block matrices, sub-matrix AP2、AP3Not square but full rank sub-square AP2 *、AP3 *And A isP2 *、AP3 *Has similar diagonal dominance; a is to beP1、AP4、AP2 *、AP3 *Is taken out and is according to it at APOf (1), reconstituting the sparse matrix AJ，AJCan be described as a four-block matrix, shaped as:
Figure FDA0002266913560000021
in the formula, S, T*、U*W is a diagonal matrix, and diagonal elements of each matrix meet the following conditions:
Figure FDA0002266913560000022
in the formula, AJThe matrix is a highly sparse matrix, sub-matrices S and W are diagonal matrices, and non-zero elements of rows and columns in the sub-matrices T and U are not more than 1 at most; to AJInversion to obtain an improved Jacobi preprocessor MJ；
The second stage of the two-stage pretreatment is specifically:
the modified equation set is further modified by a Jacobi preprocessor as follows:
APMJy＝MPb
coefficient matrix A of the quantity y to be solvedPJComprises the following steps:
APJ＝APMJ
Δx＝MJy
wherein M isJTo improve Jacobi pre-treatment.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113191105A (en) * 2021-03-22 2021-07-30 梁文毅 Electrical simulation method based on distributed parallel operation method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140046993A1 (en) * 2012-08-13 2014-02-13 Nvidia Corporation System and method for multi-color dilu preconditioner
CN106532712A (en) * 2016-12-09 2017-03-22 大连海事大学 Rectangular coordinate Newton method load flow calculation method for small-impedance-branch-containing power grid based on compensation method
CN108804386A (en) * 2018-07-09 2018-11-13 东北电力大学 A kind of parallelization computational methods of power system load nargin

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140046993A1 (en) * 2012-08-13 2014-02-13 Nvidia Corporation System and method for multi-color dilu preconditioner
CN106532712A (en) * 2016-12-09 2017-03-22 大连海事大学 Rectangular coordinate Newton method load flow calculation method for small-impedance-branch-containing power grid based on compensation method
CN108804386A (en) * 2018-07-09 2018-11-13 东北电力大学 A kind of parallelization computational methods of power system load nargin

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113191105A (en) * 2021-03-22 2021-07-30 梁文毅 Electrical simulation method based on distributed parallel operation method

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